Nick Fury's debt to Wolverine ended up saving the Ultimate X-Men in one of their darkest hours. Although the timeline and its details would be adjusted over time, Nicholas Fury and Logan would cross paths multiple times, one where the senseless killer saved Fury's life in the desert. Years later, when Fury was ascending the ranks of SHIELD, he fulfilled his debt when he followed up on Logan's call to help save him and the other X-Men from the clutches of the Weapon X program.
The Ultimate universe reimagined its characters without worrying about continuity or connections to mainstream storylines thus allowing creators to create new and exciting storylines or directions. In the Ultimate X-Men, Nick Fury's military past revealed he was assigned to the Weapon X program during the Gulf War. When a mission to escort Wolverine was interrupted by unexpected guerilla forces, Fury's battalion was killed with Fury severely wounded. Although the skirmish freed him, Wolverine killed the attackers and in a surprising show of humanity, he carried Fury through the desert to a friendly base camp. Although Logan was rewarded for his bravery by being beaten and taken back into custody, the now one-eyed Fury never forgot that and thus created a bond that would continue when Fury had become Director of SHIELD and Wolverine had joined Charles Xavier's X-Men.
In the 'Return to Weapon X' storyline by Millar, Kubert, and Tom Raney, Xavier and the X-Men were captured by Weapon X, a SHIELD-initiated program that forced mutants to complete covert missions. While they failed to capture Wolverine, Colonel John Wraith and Dr. Abraham Cornelius enjoyed forcing the X-Men to join other notable mutants like Rogue, Nightcrawler, and Juggernaut while they were regularly tortured and tested. While the latest Weapon X was useful in helping to free Fury from capture in a foreign country, they took it too far when Wraith made a move to kill General Thaddeus Ross when he threatened to cut their funding and phase the program out completely. They were eventually successful in capturing Wolverine, only to learn he had sealed their fate by leading Weapon X's enemies to their location.
According to the official timeline, Nick Fury and Logan have known each other for quite a long time. In Ultimate Origins, they were in the military together where getting arrested for looting led to Logan helping to kickstart the mutant race while Fury became his world's first super-soldier before Captain America. Despite the horrors Weapon X wrought upon James Howlett's mind as they transformed him into the savage Wolverine, his humanity remained. When he saved Fury in the desert, it was either due to unconsciously honoring their former friendship or a sign that he wasn't an animal after all. When Weapon X sought to reclaim him, Wolverine's absence endangered the X-Men, whose training was no match for the eventually rogue government outfit's resources and cruelty. Logan got the last laugh when he tricked his former captors with a tracking device that brought the latest Brotherhood to their doorstep.
In the end, Colonel John Wraith hated mutants so much that he declared war against his own government when they denied him the ability to fight against the perceived homo superior threat. Incapable of surrendering peacefully, Wraith was killed by Nick Fury who showed up with a battalion of SHIELD soldiers. When the X-Men and Brotherhood question Fury's motive and agenda, Wolverine appears to reveal that not only did he tip Fury off but he was the reason Logan escaped Weapon X in the first place. After helping the X-Men survive, Nick Fury would tap Wolverine for the occasional assignment, realizing a man of his skills could come in handy in extraordinary circumstances.